Dynamic Programming: Knapsack - Target Sum
What is the space complexity of the top-down memoized recursive solution for the Target Sum problem with input size n and total sum W = sum(nums)?
What is the space complexity of the top-down memoized recursive solution for the Target Sum problem with input size n and total sum W = sum(nums)?
medium🪤 Complexity Trap Q6 of Q15
Step-by-Step Solution
Solution:
Step 1: Analyze memoization storage
Memo stores results for states (i, current_sum), total O(n * W) entries.Step 2: Analyze recursion stack space
Recursion depth is O(n), so call stack uses O(n) space.Step 3: Combine space usage
Total space is memo + recursion stack = O(n * W) + O(n), but memo dominates, so O(n * W).Final Answer:
Option B -> Option BQuick Check:
Memo table plus recursion stack -> O(n * W) space [OK]
Quick Trick: Memo table + recursion stack -> O(n * W) space [OK]
Common Mistakes:
MISTAKES- Ignoring recursion stack space
- Assuming only memo space matters
Trap Explanation:
PITFALL- Candidates often forget recursion stack space, underestimating total space complexity.
Interviewer Note:
CONTEXT- Tests understanding of combined space usage in recursive DP.
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